Identify the pattern and the next three terms in the given sequences: 125, 250, 375, 500; 8, 24, 72; 286, 311, 336, , , .

The sequence is $125, 250, 375, 500$.

a) What is the difference between the numbers?
Calculate the difference between consecutive terms:

$$250 - 125 = 125$$ $$375 - 250 = 125$$ $$500 - 375 = 125$$

The difference between the numbers is constant.
The difference between the numbers is $\boxed{125}$.

b) Describe the pattern.
The pattern is to add 125 to the previous number. This sequence is also a list of multiples of 125.
The pattern is: Add 125 to the previous number.

The sequence is $8, 24, 72$.

a) What is the difference between the numbers?
Calculate the difference between consecutive terms:

$$24 - 8 = 16$$ $$72 - 24 = 48$$

The differences are not constant.

b) Describe the pattern.
Let's check for a multiplicative pattern:

$$24 \div 8 = 3$$ $$72 \div 24 = 3$$

The pattern is to multiply the previous number by 3.
The pattern is: Multiply the previous number by 3.

The sequence is 286, 311, 336, \text{___}, \text{___}, \text{___}.

a) Give the next three numbers of the sequence. Describe the pattern.
First, find the pattern by calculating the difference between consecutive terms:

$$311 - 286 = 25$$ $$336 - 311 = 25$$

The pattern is to add 25 to the previous number.

Now, find the next three numbers:

$$336 + 25 = 361$$ $$361 + 25 = 386$$ $$386 + 25 = 411$$

The next three numbers are $\boxed{361, 386, 411}$.
The pattern is: Add 25 to the previous number.